Low-Rank Adaptation (LoRA) has proven effective in reducing computational costs while maintaining performance comparable to fully fine-tuned foundation models across various tasks. However, its fixed low-rank structure restricts its adaptability in scenarios with substantial domain gaps, where higher ranks are often required to capture domain-specific complexities. Current adaptive LoRA methods attempt to overcome this limitation by dynamically expanding or selectively allocating ranks, but these approaches frequently depend on computationally intensive techniques such as iterative pruning, rank searches, or additional regularization. To address these challenges, we introduce Stable Rank-Guided Low-Rank Adaptation (SR-LoRA), a novel framework that utilizes the stable rank of pre-trained weight matrices as a natural prior for layer-wise rank allocation. By leveraging the stable rank, which reflects the intrinsic dimensionality of the weights, SR-LoRA enables a principled and efficient redistribution of ranks across layers, enhancing adaptability without incurring additional search costs. Empirical evaluations on few-shot tasks with significant domain gaps show that SR-LoRA consistently outperforms recent adaptive LoRA variants, achieving a superior trade-off between performance and efficiency. Our code is available at https://anonymous.4open.science/r/SR-LoRA-A18F.